Linear Diversity Combining on Nakagami-0.5 Fading Channels

The Nakagami-0.5 distribution is an important special case of the Nakagami distribution as it represents a worst case fading scenario. This scenario is of particular significance for wireless applications with high quality of service requirements. The bit error probability (BEP) performances of three basic diversity combining schemes in Nakagami-0.5 fading are considered. It is shown that the error rate performances of dual branch equal gain and selection combining (SC) diversity are identical regardless of modulation format. It is also shown that L-branch maximal ratio combining diversity in Nakagami-0.5 fading has the same BEP performance as single branch reception in Nakagami-L/2 fading with L times the transmission power of each branch. A useful upper bound for the BEP of L-branch SC diversity in Nakagami-0.5 fading is also derived. The performance degradation for the worst case Nakagami-0.5 fading relative to Rayleigh fading can be as much as 24.6 dB for a dual-diversity receiver at target BEP of 10^-6. The additional resources required to restore a specified performance level, as increased channel signal-to-noise ratio and as number of additional diversity branches, are quantified. It is concluded that worst case Nakagami channels can result in dramatically poorer performance than Rayleigh channels, making proper system design and evaluation essential to achieve a required transmission quality.